Bel联盟博弈中核心及其他解概念的性质（事前场景）
Properties of the core and other solution concepts of Bel coalitional games in the ex-ante scenario
AI总结：
本文研究了Bel联盟博弈中核心及其他解概念在事前场景下的性质，探讨了不确定性环境下合同分配与偏好建模，并发现这些解概念的包含关系与经典情况一致。
摘要：
我们研究了Bel联盟博弈中核心及其他解概念的性质，这些博弈通过在框架中引入不确定性来推广经典联盟博弈。在不确定的环境中，我们使用合同，这些合同规定了代理人在不同世界状态下的联盟价值分配方式。每个代理人都可能对真实世界状态有不同的先验知识，这通过Dempster-Shafer理论建模，而代理人之间对合同的偏好则通过Choquet积分建模。我们专注于“事前”场景，即在不确定性解决之前评估合同。我们研究了当所有代理人都有相同先验知识（即概率分布）时事前核心的几何结构。最后，我们定义了事前情况下的（预）核力、核和谈判集（Mas-Colell式），并研究了它们的性质。发现这些解概念之间的包含关系与经典情况相同。对于凸Bel联盟博弈，事前核心与事前谈判集重合，但需要加强谈判集的定义。
英文摘要：
We study the properties of the core and other solution concepts of Bel coalitional games, that generalize classical coalitional games by introducing uncertainty in the framework. In this uncertain environment, we work with contracts, that specify how agents divide the values of the coalitions in the different states of the world. Every agent can have different a priori knowledge on the true state of the world, which is modeled through the Dempster-Shafer theory, while agents' preferences between contracts are modeled by the Choquet integral. We focus on the "ex-ante" scenario, when the contract is evaluated before uncertainty is resolved. We investigate the geometrical structure of the ex-ante core when agents have the same a priori knowledge which is a probability distribution. Finally, we define the (pre)nucleolus, the kernel and the bargaining set (a la Mas-Colell) in the ex-ante situation and we study their properties. It is found that the inclusion relations among these solution concepts are the same as in the classical case. Coincidence of the ex-ante core and the ex-ante bargaining set holds for convex Bel coalitional games, at the price of strengthening the definition of bargaining sets.
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